模块化多电平换流器电磁暂态高效建模方法研究
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摘要
模块化多电平换流器高压直流输电(Modular Multilevel Converter based High Voltage Direct Current, MMC-HVDC)以其独特的技术优势,已成为未来电压源换流器高压直流输电(Voltage Source Converter based HVDC, VSC-HVDC)领域的发展趋势,将在我国电力系统中发挥重大作用。与两电平、三电平VSC-HVDC在电磁暂态(Electromagnetic Transient, EMT)仿真中采用单个器件代表整个换流阀不同,高电压、大功率的MMC-HVDC在电磁暂态仿真中必须单独仿真超大数量的开关器件,导致仿真速度非常缓慢,使得MMC-HVDC一次电路参数选取及控制系统参数的优化变得非常困难,很大地阻碍了高电平MMC-HVDC的研究进展及工程化应用。因此,深入分析MMC-HVDC的运行特性,研究开发在保证其系统仿真精度的前提下的高效建模方法,具有重大的理论及工程意义。论文针对模块化多电平换流器电磁暂态高效建模方法进行全面深入的基础研究。
1) MMC-HVDC拓扑机制及运行特性研究
为了研究MMC-HVDC的电磁暂态高效建模方法,首先分析了MMC的通用拓扑结构及三种常见子模块,也即半桥型子模块(Half-Bridge Sub-module, HBSM)、双箝位型子模块(Clamp-double Sub-module, CDSM)和全桥型子模块(Full-Bridge Sub-module, FBSM)的拓扑结构和工作模式。其次从理论上证明了不同子模块结构的MMC均适用传统同步旋转坐标系下的站级解耦控制策略,并推导了该策略在MMC中的具体表达式。进而分别介绍了传统的基于最近电平逼近控制(Nearest Level Control, NLC)和载波移相正弦脉宽调制(Carrier Phase Shifted Sinusoidal Pulse Width Modulation, CPS-SPWM)的MMC调制和电容电压平衡控制策略。
基于上述MMC站级解耦控制及调制均压策略,不同子模块结构的MMC均可以构造闭环MMC型VSC-HVDC系统。三种MMC子模块的最大区别在于切断双极直流短路故障引起的短路电流的能力不同,为了精确评估不同结构MMC切断直流故障电流的能力,提出了MMC-HVDC的直流故障穿越能力指标(DCFaults Ride-through Capability Index, DFRTI)。仿真结果表明,在相同的系统参数下, DFRTI(FBSM)> DFRTI(CDSM)>DFRTI(HBSM).以采用FBSM的3端MMC-HVDC为例,提出了具备直流故障穿越能力的多端MMC-HVDC (Multi-terminal MMC-HVDC, MMC-MTDC)系统的直流故障线路定位和隔离以及快速功率恢复的控制策略,PSCAD/EMTDC下的仿真验证了所提出控制策略的正确性和有效性。
2)基于受控源的MMC通用建模方法研究.
在仿真超大规模MMC所包含的大量子模块的开关器件时,PSCAD/EMTDC等电磁暂态仿真软件需要不断地对超高阶导纳矩阵求逆,这是其在电磁暂态仿真中速度非常缓慢的本质原因。因此,全部MMC的仿真提速模型都需要在保证仿真精度的前提下对高阶导纳矩阵进行降阶求解。
根据节点电压分析法,提出了基于受控源的MMC电磁暂态仿真提速模型,其本质为将求解MMC的每个桥臂所对应的超高阶矩阵转化为求解与桥臂内子模块数目相同的小矩阵,并使其与原有矩阵同解。因此,所提出的MMC模型可以在显著提升仿真速度的同时,精确等效MMC的外特性以及子模块的电容电压充放电过程等内部特性。所提出的模型完全采用电磁暂态仿真平台模型库中的已有元件,无需用户自定义；同时,采用节点电压法证明了该模型与原有详细模型同解,且由证明过程的一般性可知,所提出模型不仅适用于三种常见MMC在PSCAD/EMTDC下的仿真,对其余MMC结构以及诸如MATLAB/SIMULINK等电磁暂态仿真平台都具有很强的通用性。在PSCAD/EMTDC中搭建的不同电平数半桥型MMC模型验证了所提出模型的仿真精度及提速效果。
3)基于戴维南等效的MMC整体建模方法研究
在上述基于受控源的MMC通用仿真提速模型中,由于不需要用户自定义,模型中所采用的开关元件与详细模型完全相同,因此其必须与详细模型(Detailed Model, DM)采用完全相同的调制及电容电压平衡控制方法。然而,MMC-HVDC不同于两电平、三电平VSC-HVDC的一个显著特点是复杂的调制及电容电压平衡控制算法,仿真表明,控制算法的复杂度已成为制约MMC的电磁暂态仿真效率的重要因素。因此,有必要以用户自定义的形式开发MMC等效模型,并提出一种计算效率较高的MMC子模块电容均压算法。
分别以基于HBSM和FBSM的MMC为例,采用后退欧拉法(Backward Euler Method)将每个子模块的电容离散化为戴维南电压源和电阻的串联,并假设子模块中的开关器件在断开状态时为理想器件(即无穷大电阻),因此在对MMC一次电路求解时的计算量得到大大简化。同时,由于采用后退欧拉法,每个子模块电容电压的瞬时值只取决于子模块当前步长的投切状态。基于上述假设,提出了一种计算复杂度与桥臂子模块个数相同的MMC高效排序均压方法,并介绍了所提出MMC整体建模的闭锁功能实现方法,使其具备仿真换流器的启动与直流故障闭锁等功能。上述换流器及均压算法的整体建模,使MMC的计算复杂度随电平数线性变化。仿真验证表明,所提出的MMC模型及排序均压算法均具有极高的仿真精度并在上千电平时与MMC平均值模型(Averaged-value Model, AVM)的仿真效率具有可比性。最后,将所提出的整体建模方法应用到了全桥型MMC中并进行了仿真验证。
4)MMC平均值模型在直流电网中的应用研究
在前述两类MMC模型中,子模块电容充放电特性得以精确体现,因此其外部特性与MMC详细模型完全相同。然而,MMC的平均值模型分别采用受控电压源与电流源来等效MMC详细模型的交、直流侧,且采用平均化技术,只有一个直流侧等效电容,因此其无法仿真详细模型内部每个子模块的充放电特性,一般用于多端直流电网的系统级高效仿真。由于MMC详细模型的非线性运行特性非常复杂,而平均值模型对其进行了很大的简化,因此分析研究平均值模型的适用性是很有意义的。
以采用MMC详细模型搭建的4端直流电网为基准,对比发现平均值模型有效的前提是相对应的详细模型中的子模块电容值足够大,以使其全部电容电压几乎恒定。同时,分析发现不同的MMC调制及均压算法对平均值模型的适用性无明显影响,但使用平均值模型所带来的加速比却随着调制均压算法的计算复杂度而上升。同时,原有平均值模型无法精确仿真直流故障特性及换流器闭锁等多端直流电网仿真中的必备功能。为了弥补这一不足,提出了改进平均值模型拓扑,仿真表明其可以满足直流电网的各种仿真需求。虽然本文以半桥型MMC平均值模型为例,但是所提出的平均值模型适用性分析方法和拓扑改进措施对另外两种MMC平均值模型也具有理论指导意义。
Modular Multilevel Converter based High Voltage Direct Current (MMC-HVDC) is playing an more and more important role in the power system of China, and it has become the development trend of the Voltage Source Converter based HVDC (VSC-HVDC), due to its special technical advantages. In the Electromeganetic Transient (EMT) programs, such as PSCAD/EMTDC, the conventional2or3-level VSC-HVDC uses single semiconductor to represent the whole multi-valve. However, the ultral-high voltage and power ratings MMC-HVDC has to simulate the large number of sub-modules (SMs) in each multi-valve individually, which makes the EMT-type simulations extremely slow and the circuit parameters selection and optimization of control systems extremely difficult. Furthermore, it constitutes enormous obstacles for the research of ultral-large MMC-HVDC systems and their engineering applications. Therefore, it is of great theoretical and engineering values to analyze the operational characteristics of MMC-HVDC and propose the EMT-type efficient modelling methods of MMC with the simulation accuracy preserved, which is investigated fundamentally and comprehensively in this dissertation.
1) Research on the topology mechanisms and operational characteristics of MMC-HVDC
For the purpose of investigating the EMT-type efficient modelling methods of MMC, the universal topology of MMC and the working modes of the three common sub-module implementations, including Half-Bridge Sub-module (HBSM), Clamp-Double Sub-module (CDSM) and Full-Bridge Sub-module (FBSM) are analyzed. This paper theoretically demonstrated that the traditional dq axis based decoupled control strategies are applicable to the three sub-modules based MMCs, and further deduced the specific control formulas for MMC. Then the Nearest Level Control (NLC) and Carrier Phase Shifted Sinusoidal Pulse Width Modulation (CPS-SPWM) based MMC internal modulation and capacitor voltage balancing algorithms are presented.
Based on the above MMC internal control algorithms, the different sub-modules based MMCs can be constructed to closed-loop control MMC-HVDC systems. The essential metrics of the three sub-modules are the capabilities to suppress the short circuit currents under DC pole to pole short circuit fault. Hence the DC Faults Ride-through Capability Index (DFRTI) is proposed to evaluate such capabilities precisely. Simulations show that under the same system configuration, DFRTI(FBSM)> DFRTI(CDSM)> DFRTI(HBSM). Taking the FBSM based3-terminal MMC-HVDC to exemplify, the DC faults location, isolation and fast power recovery schemes for the multi-terminal MMC-HVDC (MMC-MTDC) which is capable of riding through the severe DC faults are proposed and simulations in PSCAD/EMTDC valitated its correctness and effectiveness.
2) Research on the controlled source based universal modelling method of MMC
With the ultral-large number of semeconductor components in the large scale MMC switch on and off alternatively, the EMT-type programs has to inverse the large order admittance matrix constantly, this is why it takes extremely long time to simulate ultral-large MMC-HVDC system on EMT-type programs. Therefore, all the accelerated MMC models have to reduce the matrix order of the MMC converters with the simulation accuracy preserved.
Based on the Node Voltage Analysis method, the controlled source based EMT-type MMC accelerated model is proposed. The essence of the new model is the partition of one large-scale admittance matrix into substantial small-scale matrices which provide the equivalent solutions; hence it guarantees the accuracy of the MMC external and internal behaviros. Meanwhile, the computation burden of MMC is significantly reduced, as compared to the full detailed model. The proposed MMC model uses the existing building blocks in the user library of the EMT-type program, no need for user-defined modules. Therefore, the new model is not only suitable for the three types sub-modules based MMC systems on PSCAD/EMTDC, but also other multi-level converters on other EMT-type programs. Finally, the HBSM based MMC models on PSCAD/EMTDC valitates the accuracy and speed-up factor of the proposed model.
3) Research on the Thevenin's equivalent based overall modelling of MMC
There is no need for user-defined module in the above controlled source based MMC model; hence the building blocks as well as the modulation and capacitor voltage balancing algorithms are the same as the full detailed model. However, one of the remarkable features that MMC-HVDC compared to2or3-level VSC-HVDC is the complex voltage balancing algorithms, and simulations have shown that it does have great impact on the computation efficiency of MMC simulating on EMT-type programs. To solve the problem, this paper proposes the user-difined Thevenin's equivalent MMC model and the highly efficient sorting based balancing algorithm to overall model the MMC system.
Taking the HBSM and FBSM based MMC models to exemplify, using the Backward Euler Method to discretize the capacitor in each sub-module to the series connection of the Thevenin's equivalent voltage source and resistance, and assuming the switches to be ideal (i.e. infinite resistance) if they are switched off, hence the computation complexity of the converter is significantly reduced. Meanwhile, as Backward Euler Method is applied to the capacitors, the instantaneous capacitor voltage of each sub-module is determined by only one time step history knowledge of its switching state. Then an efficient MMC capacitor voltage sortinig algorithm whose computation burden increases linearly with the number of the MMC sub-modules is proposed, and the blocking mode implementation of the proposed MMC model is introduced. The CPU efficiency of the overall MMC model is in direct proportion to the simulation scale. Also the MMC model which is composed of the improved converter and the tranditional CPS-SPWM control algorithm is also implemented and validated. Simulations on PSCAD/EMTDC show that the proposed MMC models are comparable with corresponding Averaged-value Model (AVM) in CPU efficiency for the case of MMC model with more than one thoudand sub-modules per arm. Finally, the proposed overall modeling method is extended to full-bridge MMC and its accuracy is validated.
4) Research on the use of the averaged-value model of MMC in DC grid
In the above proposed controlled source and Thevenin's equivalent based models, the MMC internal capacitor charging and discharging characteristics are precisely simulated, hence their external behaviors are identical to the full detailed MMC models. However, the averaged-value MMC model uses controlled voltage sources and current sources to represent the AC and DC sides of the Detailed Model (DM). The AVM applies averaging technique and has only one equivalent capacitor, thus it cannot simulate the MMC internal charging and discharging characteristics of each capacitor in DM and quite suitable for efficient system-level simulation of multi-terminal DC grid. However, due to the strong nonlinearity and complex operational characteristics of the DM, the applicability of the AVM needs strict proof to avoid misuse.
The HBSM based AVM is benchmarked by comparison with a4-terminal DM based MMC-HVDC grid. Analysis results show that the AVM is just effective when the capacitors are large enough to maintain nearly constant voltage across each MMC sub-module. The type of MMC internal modulation and voltage balancing scheme does not appear to have significant impact on the validity of the model, but the speed-up afforded by the AVM is more when a more complex voltage scheme is in effect. Due to the topological reasons, the previously developed AVM cannot simulate dc faults as well as MMC blocking behaviors properly, as would be required for multi-terminal DC grid simulations. To address this issue, the paper proposed the improved AVM which is shown to work well simulating all DC grid operating conditions. The applicability analysis method and improvements for the HBSM based AVM is with an important reference for CDSM and FBSM based AVMs.
1) MMC-HVDC拓扑机制及运行特性研究
为了研究MMC-HVDC的电磁暂态高效建模方法,首先分析了MMC的通用拓扑结构及三种常见子模块,也即半桥型子模块(Half-Bridge Sub-module, HBSM)、双箝位型子模块(Clamp-double Sub-module, CDSM)和全桥型子模块(Full-Bridge Sub-module, FBSM)的拓扑结构和工作模式。其次从理论上证明了不同子模块结构的MMC均适用传统同步旋转坐标系下的站级解耦控制策略,并推导了该策略在MMC中的具体表达式。进而分别介绍了传统的基于最近电平逼近控制(Nearest Level Control, NLC)和载波移相正弦脉宽调制(Carrier Phase Shifted Sinusoidal Pulse Width Modulation, CPS-SPWM)的MMC调制和电容电压平衡控制策略。
基于上述MMC站级解耦控制及调制均压策略,不同子模块结构的MMC均可以构造闭环MMC型VSC-HVDC系统。三种MMC子模块的最大区别在于切断双极直流短路故障引起的短路电流的能力不同,为了精确评估不同结构MMC切断直流故障电流的能力,提出了MMC-HVDC的直流故障穿越能力指标(DCFaults Ride-through Capability Index, DFRTI)。仿真结果表明,在相同的系统参数下, DFRTI(FBSM)> DFRTI(CDSM)>DFRTI(HBSM).以采用FBSM的3端MMC-HVDC为例,提出了具备直流故障穿越能力的多端MMC-HVDC (Multi-terminal MMC-HVDC, MMC-MTDC)系统的直流故障线路定位和隔离以及快速功率恢复的控制策略,PSCAD/EMTDC下的仿真验证了所提出控制策略的正确性和有效性。
2)基于受控源的MMC通用建模方法研究.
在仿真超大规模MMC所包含的大量子模块的开关器件时,PSCAD/EMTDC等电磁暂态仿真软件需要不断地对超高阶导纳矩阵求逆,这是其在电磁暂态仿真中速度非常缓慢的本质原因。因此,全部MMC的仿真提速模型都需要在保证仿真精度的前提下对高阶导纳矩阵进行降阶求解。
根据节点电压分析法,提出了基于受控源的MMC电磁暂态仿真提速模型,其本质为将求解MMC的每个桥臂所对应的超高阶矩阵转化为求解与桥臂内子模块数目相同的小矩阵,并使其与原有矩阵同解。因此,所提出的MMC模型可以在显著提升仿真速度的同时,精确等效MMC的外特性以及子模块的电容电压充放电过程等内部特性。所提出的模型完全采用电磁暂态仿真平台模型库中的已有元件,无需用户自定义；同时,采用节点电压法证明了该模型与原有详细模型同解,且由证明过程的一般性可知,所提出模型不仅适用于三种常见MMC在PSCAD/EMTDC下的仿真,对其余MMC结构以及诸如MATLAB/SIMULINK等电磁暂态仿真平台都具有很强的通用性。在PSCAD/EMTDC中搭建的不同电平数半桥型MMC模型验证了所提出模型的仿真精度及提速效果。
3)基于戴维南等效的MMC整体建模方法研究
在上述基于受控源的MMC通用仿真提速模型中,由于不需要用户自定义,模型中所采用的开关元件与详细模型完全相同,因此其必须与详细模型(Detailed Model, DM)采用完全相同的调制及电容电压平衡控制方法。然而,MMC-HVDC不同于两电平、三电平VSC-HVDC的一个显著特点是复杂的调制及电容电压平衡控制算法,仿真表明,控制算法的复杂度已成为制约MMC的电磁暂态仿真效率的重要因素。因此,有必要以用户自定义的形式开发MMC等效模型,并提出一种计算效率较高的MMC子模块电容均压算法。
分别以基于HBSM和FBSM的MMC为例,采用后退欧拉法(Backward Euler Method)将每个子模块的电容离散化为戴维南电压源和电阻的串联,并假设子模块中的开关器件在断开状态时为理想器件(即无穷大电阻),因此在对MMC一次电路求解时的计算量得到大大简化。同时,由于采用后退欧拉法,每个子模块电容电压的瞬时值只取决于子模块当前步长的投切状态。基于上述假设,提出了一种计算复杂度与桥臂子模块个数相同的MMC高效排序均压方法,并介绍了所提出MMC整体建模的闭锁功能实现方法,使其具备仿真换流器的启动与直流故障闭锁等功能。上述换流器及均压算法的整体建模,使MMC的计算复杂度随电平数线性变化。仿真验证表明,所提出的MMC模型及排序均压算法均具有极高的仿真精度并在上千电平时与MMC平均值模型(Averaged-value Model, AVM)的仿真效率具有可比性。最后,将所提出的整体建模方法应用到了全桥型MMC中并进行了仿真验证。
4)MMC平均值模型在直流电网中的应用研究
在前述两类MMC模型中,子模块电容充放电特性得以精确体现,因此其外部特性与MMC详细模型完全相同。然而,MMC的平均值模型分别采用受控电压源与电流源来等效MMC详细模型的交、直流侧,且采用平均化技术,只有一个直流侧等效电容,因此其无法仿真详细模型内部每个子模块的充放电特性,一般用于多端直流电网的系统级高效仿真。由于MMC详细模型的非线性运行特性非常复杂,而平均值模型对其进行了很大的简化,因此分析研究平均值模型的适用性是很有意义的。
以采用MMC详细模型搭建的4端直流电网为基准,对比发现平均值模型有效的前提是相对应的详细模型中的子模块电容值足够大,以使其全部电容电压几乎恒定。同时,分析发现不同的MMC调制及均压算法对平均值模型的适用性无明显影响,但使用平均值模型所带来的加速比却随着调制均压算法的计算复杂度而上升。同时,原有平均值模型无法精确仿真直流故障特性及换流器闭锁等多端直流电网仿真中的必备功能。为了弥补这一不足,提出了改进平均值模型拓扑,仿真表明其可以满足直流电网的各种仿真需求。虽然本文以半桥型MMC平均值模型为例,但是所提出的平均值模型适用性分析方法和拓扑改进措施对另外两种MMC平均值模型也具有理论指导意义。
Modular Multilevel Converter based High Voltage Direct Current (MMC-HVDC) is playing an more and more important role in the power system of China, and it has become the development trend of the Voltage Source Converter based HVDC (VSC-HVDC), due to its special technical advantages. In the Electromeganetic Transient (EMT) programs, such as PSCAD/EMTDC, the conventional2or3-level VSC-HVDC uses single semiconductor to represent the whole multi-valve. However, the ultral-high voltage and power ratings MMC-HVDC has to simulate the large number of sub-modules (SMs) in each multi-valve individually, which makes the EMT-type simulations extremely slow and the circuit parameters selection and optimization of control systems extremely difficult. Furthermore, it constitutes enormous obstacles for the research of ultral-large MMC-HVDC systems and their engineering applications. Therefore, it is of great theoretical and engineering values to analyze the operational characteristics of MMC-HVDC and propose the EMT-type efficient modelling methods of MMC with the simulation accuracy preserved, which is investigated fundamentally and comprehensively in this dissertation.
1) Research on the topology mechanisms and operational characteristics of MMC-HVDC
For the purpose of investigating the EMT-type efficient modelling methods of MMC, the universal topology of MMC and the working modes of the three common sub-module implementations, including Half-Bridge Sub-module (HBSM), Clamp-Double Sub-module (CDSM) and Full-Bridge Sub-module (FBSM) are analyzed. This paper theoretically demonstrated that the traditional dq axis based decoupled control strategies are applicable to the three sub-modules based MMCs, and further deduced the specific control formulas for MMC. Then the Nearest Level Control (NLC) and Carrier Phase Shifted Sinusoidal Pulse Width Modulation (CPS-SPWM) based MMC internal modulation and capacitor voltage balancing algorithms are presented.
Based on the above MMC internal control algorithms, the different sub-modules based MMCs can be constructed to closed-loop control MMC-HVDC systems. The essential metrics of the three sub-modules are the capabilities to suppress the short circuit currents under DC pole to pole short circuit fault. Hence the DC Faults Ride-through Capability Index (DFRTI) is proposed to evaluate such capabilities precisely. Simulations show that under the same system configuration, DFRTI(FBSM)> DFRTI(CDSM)> DFRTI(HBSM). Taking the FBSM based3-terminal MMC-HVDC to exemplify, the DC faults location, isolation and fast power recovery schemes for the multi-terminal MMC-HVDC (MMC-MTDC) which is capable of riding through the severe DC faults are proposed and simulations in PSCAD/EMTDC valitated its correctness and effectiveness.
2) Research on the controlled source based universal modelling method of MMC
With the ultral-large number of semeconductor components in the large scale MMC switch on and off alternatively, the EMT-type programs has to inverse the large order admittance matrix constantly, this is why it takes extremely long time to simulate ultral-large MMC-HVDC system on EMT-type programs. Therefore, all the accelerated MMC models have to reduce the matrix order of the MMC converters with the simulation accuracy preserved.
Based on the Node Voltage Analysis method, the controlled source based EMT-type MMC accelerated model is proposed. The essence of the new model is the partition of one large-scale admittance matrix into substantial small-scale matrices which provide the equivalent solutions; hence it guarantees the accuracy of the MMC external and internal behaviros. Meanwhile, the computation burden of MMC is significantly reduced, as compared to the full detailed model. The proposed MMC model uses the existing building blocks in the user library of the EMT-type program, no need for user-defined modules. Therefore, the new model is not only suitable for the three types sub-modules based MMC systems on PSCAD/EMTDC, but also other multi-level converters on other EMT-type programs. Finally, the HBSM based MMC models on PSCAD/EMTDC valitates the accuracy and speed-up factor of the proposed model.
3) Research on the Thevenin's equivalent based overall modelling of MMC
There is no need for user-defined module in the above controlled source based MMC model; hence the building blocks as well as the modulation and capacitor voltage balancing algorithms are the same as the full detailed model. However, one of the remarkable features that MMC-HVDC compared to2or3-level VSC-HVDC is the complex voltage balancing algorithms, and simulations have shown that it does have great impact on the computation efficiency of MMC simulating on EMT-type programs. To solve the problem, this paper proposes the user-difined Thevenin's equivalent MMC model and the highly efficient sorting based balancing algorithm to overall model the MMC system.
Taking the HBSM and FBSM based MMC models to exemplify, using the Backward Euler Method to discretize the capacitor in each sub-module to the series connection of the Thevenin's equivalent voltage source and resistance, and assuming the switches to be ideal (i.e. infinite resistance) if they are switched off, hence the computation complexity of the converter is significantly reduced. Meanwhile, as Backward Euler Method is applied to the capacitors, the instantaneous capacitor voltage of each sub-module is determined by only one time step history knowledge of its switching state. Then an efficient MMC capacitor voltage sortinig algorithm whose computation burden increases linearly with the number of the MMC sub-modules is proposed, and the blocking mode implementation of the proposed MMC model is introduced. The CPU efficiency of the overall MMC model is in direct proportion to the simulation scale. Also the MMC model which is composed of the improved converter and the tranditional CPS-SPWM control algorithm is also implemented and validated. Simulations on PSCAD/EMTDC show that the proposed MMC models are comparable with corresponding Averaged-value Model (AVM) in CPU efficiency for the case of MMC model with more than one thoudand sub-modules per arm. Finally, the proposed overall modeling method is extended to full-bridge MMC and its accuracy is validated.
4) Research on the use of the averaged-value model of MMC in DC grid
In the above proposed controlled source and Thevenin's equivalent based models, the MMC internal capacitor charging and discharging characteristics are precisely simulated, hence their external behaviors are identical to the full detailed MMC models. However, the averaged-value MMC model uses controlled voltage sources and current sources to represent the AC and DC sides of the Detailed Model (DM). The AVM applies averaging technique and has only one equivalent capacitor, thus it cannot simulate the MMC internal charging and discharging characteristics of each capacitor in DM and quite suitable for efficient system-level simulation of multi-terminal DC grid. However, due to the strong nonlinearity and complex operational characteristics of the DM, the applicability of the AVM needs strict proof to avoid misuse.
The HBSM based AVM is benchmarked by comparison with a4-terminal DM based MMC-HVDC grid. Analysis results show that the AVM is just effective when the capacitors are large enough to maintain nearly constant voltage across each MMC sub-module. The type of MMC internal modulation and voltage balancing scheme does not appear to have significant impact on the validity of the model, but the speed-up afforded by the AVM is more when a more complex voltage scheme is in effect. Due to the topological reasons, the previously developed AVM cannot simulate dc faults as well as MMC blocking behaviors properly, as would be required for multi-terminal DC grid simulations. To address this issue, the paper proposed the improved AVM which is shown to work well simulating all DC grid operating conditions. The applicability analysis method and improvements for the HBSM based AVM is with an important reference for CDSM and FBSM based AVMs.
引文
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